EXPERIMENTAL STUDY OF ION THRUSTER OPERATION WITH OXYGEN AS THE PROPELLANT by ROBERT BARTOLDO AGUTLAR B.S.A.E., University of Arizona (1981) SUBMITTED TO THE DEPARTMENT OF AERONAUTICS AND ASTRONAUTICS IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN AERONAUTICS AND ASTRONAUTICS at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 1983 Q Massachusetts Institute of Technology Signature of Author 7-) Certified by Accepted by Department of Aeronautics and Astronautics Professor Manuel Martinez-Sanchez T esis Supervisor Profess4 Harold Y. Wachman Chairman, Departmental Graduate Committee Archives MASSACHUSETS MSTITUTE OF ECHNOLY MAY 1 7 1983 LIBRARIES
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EXPERIMENTAL STUDY OF ION THRUSTER OPERATION WITH
OXYGEN AS THE PROPELLANT
by
ROBERT BARTOLDO AGUTLAR
B.S.A.E., University of Arizona(1981)
SUBMITTED TO THE DEPARTMENT OFAERONAUTICS AND ASTRONAUTICSIN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THEDEGREE OF
MASTER OF SCIENCE INAERONAUTICS AND ASTRONAUTICS
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May 1983
Q Massachusetts Institute of Technology
Signature of Author
7-)
Certified by
Accepted by
Department of Aeronauticsand Astronautics
Professor Manuel Martinez-SanchezT esis Supervisor
Profess4 Harold Y. WachmanChairman, Departmental
Graduate Committee
ArchivesMASSACHUSETS MSTITUTE
OF ECHNOLY
MAY 1 7 1983
LIBRARIES
EXPERIMENTAL STUDY OF ION THRUSTER OPERATION WITH
OXYGEN AS THE PROPELLANT
by
ROBERT BARTOLDO AGUILAR
Submitted to the Department of Aeronautics and Astronautics
on May 12, 1983 in partial fulfillment of the
requirements for the Degree of Master of Science in
Aeronautics and Astronautics
ABSTRACT
An experimental study was performed on a six
centimeter (anode diameter) ion thruster using oxygen as the
propellant. The engine is of the electron bombardment type
and employs a thermionic (filament) cathode. A tapered
magnetic field is supplied by windings of insulated wire. The
focus of the study is on plasma diagnostics using cylindrical
Langmuir probes. Their use in flowing plasmas and electro-
negative gases is discussed.
Several tests were performed analyzing the varia-
tion of discharge chamber and stream plasma properties
(electron density, electron temperature, and plasma space-
charge potential) with engine operating parameters such as
neutral flowrate, magnetic field strength,.and accelerator
grid potential. Also presented are the radial distributions
of plasma properties in the discharge chamber and in the beam
region.
The estimated maximum propellant utilization
efficiency was found to be 6 f and the estimated thrust was
58 micronewtons. The equivalent neutral flowrate varied
between 80.1 and 299.3 mA.
Thesis Supervisor: Dr. Manuel Martinez-Sanchez
Title: Professor of Aeronautics and Astronautics
2
Acknowledgements
I would like, at this time, to thank all of the people
who directly or indirectly assisted me during the course of
this study. First of all, I wish to thank Professor Martinez-
Sanchez for sharing his knowledge and directing me in this
interesting project. Our often lengthy discussions proved to
be most enlightening and helped to tie theory and experiment
together. I also wish to apologize for the lunches delayed
on my behalf.
I would also like to thank Mr. Paul Bauer for his in-
valuable advice in the laboratory. His willingness to answer
my many questions and to supply much of the required equip-
ment is greatly appreciated.
My thanks also go to the UROP students who assisted at
various times. I especially wish to thank Mr. Alex Mayer of
Tufts University for volunteering an entire summer to the
project. Such a sacrifice cannot go unmentioned.
And lastly, I wish to.thank my parents, Manuel and
Lupe Aguilar, and all my family and friends in Arizona for
their moral support. It makes the job that much easier know-
ing you have someone who backs you, even if only in spirit.
3
LIST OF SYMBOLS
Ap Pprobe collection area
B magnetic field strength
ce average electron speed
C+ average positive ion speed
c_ average negative ion speed
F screen open area fraction
IA anode collection current
I B beam current
IBF magnetic winding current
I C cathode emission current
I, eelectron current
Ig Gaccelerator grid impingement current
IN neutralizer emission current
I 0 equivalent neutral current
Ip Pnet probe collection current
IW ion current to outer body
I+ ion current
je electron current density
jp net probe current density
j+ ion current density
L probe length
l s sheath thickness
ND Debye length
n e electron density
nm maxwellian electron density
4
n primary electron density
n+ positive ion density
n_ negative ion density
R probe radius
rL Larmor radius
Te electron temperature
T+ positive ion temperature
T_ negative ion temperature
U beam velocity
vB Bohm velocity
vBM modified Bohm velocity
V accelerator grid potential
VN net acceleration potential
VOC zero current probe potential
VP probe potential
VR reference potential
VS plasma space charge potential
LIST OF CONSTANTS
e electron charge magnitude
(1.602 x 10-19 C)
e 0permittivity of free space
(8.85 x 10 -12 C2 .N-1 .m-2)
k Boltzmann's constant
(1.38 x 10- 23 J-K~4 )
me electron mass
(9.11 x 10-31 kg)
5
M+ positive ion mass (02 +
(5.32 x 10 -26kg)
m- negative ion mass (0~)
(2.66 x 10-26 kg)
u 0permeability of a vacuum
(12.57 x 10-12 Wb-1A.m~)
6
TABLE OF CONTENTS
I. Introduction .....................
1.1 Ton Propulsion*..................
1.2 Ion Engine Research..............
1.3 Evolution of Current Study.......
1.4 Terrestrial and Extraterrestrial
Oxygen Sources...................
II.
2.1
2.2
2.4
.5
. 6
III.
3.1
3.2
3. 33.4
3.3.63.7
IV.
4.1
4.2
4.3
4.4
Electron Bombardment Thruster
General Theory...............
The Oxygen Plasma...........
Modified Bohm Velocity.......
Positive and Negative Ion
Production Rates.............
00~0
Operation.........
.................. O ~
.. *...............B
Determination of Beam Velocity and Thrust......
Concept of Electron Trap in the Beam,...........
Plasma Diagnostics Using Langmuir Probes.......
Basic Probe Theory.............................
Determination of ne , Te , and .
Effect of Ion Beam On Probe Response...........
Effect of Negative Ions On Probe Response......
Sheath Thickness...............................
Orbital Motion Limit.......................Effect of Magnetic Field On Probe Response.....
negligible compared to the former). These high energy elec-
trons are called the "primaries" and will be denoted by the
subscript "p". Once within the plasma, they collide with
neutral atoms and molecules, ions, and other electrons. The
results of these collisions include excitation, attachment,
and ionization. The primaries lose part of their energy at
each collision. These, along with electrons liberated in
ionization and other processes, become the constituents of
the second electron group, the "maxwellians" (subscript "m").
This is due to the fact that they usually exhibit a Maxwel-
lian energy distribution. Also, their temperature is general-
ly higher in smaller engines10 . In an experiment involving
an argon thruster3 and in an experiment on an oxygen glow4
discharge , two distinct maxwellian groups were identified.
Of course, it is desirable to maximize the positive
ion production rate. This is usually done by sizing the ca-
thode sheath potential so that the primaries enter the plasma
with that energy associated with the maximum ionization cross
section. Since it is known that the plasma is at a potential
which is higher than the anode, the anode potential may be
set at a level which is just lower than the optimum electron
energy level. The cathode sheath will then possess the re-
quired potential rise.
19
2.2 The Oxygen Plasma
The oxygen plasma differs from the typical ion engine
discharge chamber plasma in that it contains a substantial
number of negative ions. Oxygen is electronegative meaning
that it has an affinity for electrons. This affinity can be
attributed to oxygen's nearly complete outer electron shell.
The ions typically present in this plasma are: 02, 0 , Q ,4
and 02. Thompson found that in the positive column of an
oxygen glow discharge, the ratios of these species were:
(0~)/(0+) = 0.9; (0+)/(02) = 0.014; and
(0~)/(0~) = 0.1
where ( ) indicates specie density. The first ratio indi-cates that the density of negative ions is nine times that
of electrons for plasma neutrality to exist. It should be
noted for comparison purposes that these values were ob-
tained in a glow'discharge at a pressure of approximately
0.04 torr and with currents of 1 to 100 mA.
The creation and loss mechanisms have also been ana-
lyzed . 0~ is created primarily in the processes:
02 + e----0 + 0~ Dissociative attachment
02 + e--+-0+ + 0 Polar dissociation .
Since the plasma is at a potential which is usually higher
than any other surface bounding it, it contains the nega-
tive ions very effectively. The loss mechanism for 0~ has
been found to be mainly "associative detachment":
0 + O~ --- 02 + e
0+ is produced in polar dissociation and in the process:
0 + e --- 0 + + 2e Monatomic ionization
20
0+ is lost through charge transfer to 02, to wall migration,
and to the ion beam. 0 is created in the molecular ioniza-
tion process:
0 + e -- 0 + 2e
and is lost in migration to enclosing surfaces, to the beam,
and to the process:
0~ + 0 -0 + 0 Charge transfer
Monatomic oxygen is created both in dissociation and in
dissociative attachment. Its loss is due primarily to wall
migration.
In addition, metastables (e.g. 02 (a ag)) may have a
11considerable effect, according to Laska and Masek .These
02 (a Ag) take part in the creation of both positive and
negative ions in processes similar to those involving 02*
The energy required to attain this excited state is 0.98 eV
per molecule4 .
For the purposes of this study, it will be assumed
that the plasma is composed of only 0~ and 0+ ions along
with neutrals and electrons. The beam will be assumed to
contain only 0+ ions. This assumption, based on the above
information, appears to be fairly valid. With this in mind,
the anode voltage may be set as previously discussed. The
ionization cross section for 02 has a maximum value at an12
electron energy of approximately 125 eV . During exper-
imentation, the anode was set at a potential of 125 volts.
21
2.3 Modified Bohm Velocity
The loss rate of ions from the discharge chamber plas-
ma is determined by the ion density and by a quantity known
as the "Bohm velocity". This is the velocity at which ions
drift towards the sheaths under the influence of electrons
in a so-called pre-sheath. With only positive ions and elec-
trons present, it has a value of'3 :
vB = [(qkTm(1+np))/(em+nm)]1 (2.1)
where q is the ion charge, e is the absolute value of the
electron charge, k is the Boltzmann constant, m+ is the ion
mass, nP is the primary electron density, nm is the max-
wellian electron density, and Tm is the maxwellian electron
temperature. This would apply to engines operating on
propellants such as mercury and argon. However, in the pre-
sence of negative ions, it must be modified.
Near a negative surface, the potential (plasma)
begins to fall. When it has reached a point at which e-V
is greater than the energy of. the primary electrons, only
ions will be present. Before this point is reached, the
density of maxwellian electrons is given by:
nm(x) = nmexp [eV(x)/kTm] (2.2)
where nm will be taken to be the electron density within
the plasma, V(x) is the plasma potential at x, nm(x) is the
maxwellian electron density at x, and x being the location
within the presheath. Likewise, since negative ions are
effectively contained by the sheath drop, the negative ion
distribution is given by:
n_(x) = n-exp[eV(x)/kT] (2.3)
where n_ is the negative ion density in the plasma and T_ is
22
the negative ion temperature. The streaming positive ion
density distribution is found from continuity to be:
n+(x) = n+V+ V+(x) (2.4)
where n+ is the positive ion density in the plasma, v+ is
the positive ion velocity at the edge of the sheath, and
v+(x) is the positive ion velocity within the presheath.
From conservation of energy:
eV(x) + km +(x) 2 = Lm v 2 (2.5)
so that:
v+(X) V+ +2-2eV(x)/m+ 2 (2.5)
Inserting (2.2) into (2.1) and cancelling appropriate terms:
2 1n,(x) = n+/ {1-2eV(x)/m+v+ ]2 (2.6)
Over the region under consideration, the density of the
primaries may be assumed to be the same as in the plasma
due to their high energy. Assuming that the presheath is
still neutral, the following must hold:
n+(x) = n_(x) + n + nm(x) (2.7)
Also:
n+ = n_ + np + nm (2.8)
From (2.2), (2.3), (2.6), and (2.7):
n+/[1-2eV(x)/m+v+ nmexp[eV(x)/kTml
+ n-exp[eV(x)/kT_ + np (2.9)
23
For small values of V(x), (2.9) can be expanded to give:
n. 1+eV(x)/m+v+2] = nj1+eV(x)/kTm
+ n_ [1+eV(x)/kT_) + np (2.10)
ignoring higher order terms. Noting (2.8), cancelling V(x),
and solving for v+ yields:
v = tn+/ m+(nm/kTm + n/kT)]2 (2.11)
This is the Bohm velocity modified to account for negative
ions and will be denoted as "v BM". In practice, it yields
a value which is lower than VB and of the same magnitude as
the ion thermal velocity, c+. The loss rate to a negative
surface is thus given by:
I+ = en+AvB (normal plasma) (2.12a)
= en+AvBM (electronegativeplasma) (2.12b)
where A is the area of the surface.
24
2.4 Positive and Negative Ton Production Rates
The approximate rates of production of both the posi-
tive and negative ions may be calculated using available
cross section data. The rate of production of positive ions
per unit volume, R+, can be expressed in the form:
R+= nn npP(Ep) + nmQ+(Tm) (2.13)
where nn is the number density of neutrals, P+ is the pri-
mary rate factor, Q+ is the maxwellian rate factor, and Epis the primary electron energy. Similarly, the rate of pro-
duction of negative ions per unit volume, R_, is of the form:
R_= nn[npP_(Ep) + nmK-(Tm)l (2.14)
where P and Q_ are the rate factors associated with nega-
tive ion production. The rate factors are defined as the
product of the cross section and the electron velocity, v,
integrated over the appropriate distribution function (max-
wellian in the case of the maxwellian electrons and delta
function in the case of the primary electrons). The equa-
tions are as follow:
P = vcr(E ) (2.15a)Cop
Q = va(E)f(E)dE (2.15b)
where a is the cross section and f(E) denotes the maxwellian
distribution function. Using data obtained from References
4 and 12 and the Trapezoidal Rule (in calculating Q), the
following values are obtained:
P+(125.9 eV) = 1.82 x 10-13 m3 .s-1
Q,(30 eV) = 6.09 x lo1 4 m3 .s-1
P_(125 eV) = 1.82 x 10-16 m3 .s-1
(Polar dissociation)
25
Q_(30 eV) = 7.82 x 10-18 m3 -s~
(Dissociative attachment)
Q_(30 eV) = 1.10 x 10-16 m3 -s~
(Polar dissociation)
Note that there are two values for Q_ corresponding to the
two processes in which negative ions may be formed from
neutrals: dissociative attachment and polar dissociation.
It should also be noted that cross section data for the
polar dissociation process exists in Reference 4 only up
to an electron energy of 55 eV and so an extrapolation ofavailable data was used in calculating P_ and Q_(polar
dissociation).
It is evident that R+>> R_ because of the higher rate
factors involved. This would lead one to assume that the
negative ion population builds up to a certain steady state
level at which the rate of production just equals the rate
of losses to processes such as associative detachment. The
positive ions, on the other hand, can migrate to the walls
or be extracted in the beam.
Note: The ion production rates, R, and R, refer to the pro-
duction of 02 and 0~ from neutrals, respectively.
26
2.5 Determination of Beam Velocity and Thrust
The velocity of the ion beam, U, is determined by the
plasma potentials of the beam and discharge chamber. Refer-
ring to Figure 2.5-1, it can be seen that ions falling into
the screen sheath and successfully extracted are accelerated
to the accelerator and then decelerated once they leave the
engine by a potential rise. The final velocity attained by
the ions can be found by equating the kinetic energy to the
energy acquired in the electric field:
im+U2 = N (2.16)
where VN is the net acceleration voltage and is equal to
VS(chamber) - VS(stream). Solving for the beam velocity
gives:
U = (2eVN/m+) 2 (2.17)
The thrust is approximately equal to 1:
T = ;U (2.18)
where m is the mass expelled per unit time. If the beam
current, IB' is known, the thrust is then equal to:
T = IBMU/q (2.19)
where M is the ion molecular mass.
27
chamberpotenti
screen grid VNpotential
stream potential
acceleratorgrid potential
thruster
eacceleratorgrid
screen grid
Figure 2.5-1 Axial Potential Variation
28
i
2.6 Concept of Electron Trap in the Beam
The potential variation in the beam is typically as
shown in Figure 2.6-1. The beam plasma potential is higher
than that of the accelerator and neutralizer in a properly
designed engine. Electrons are prevented from traveling
upstream to the engine by the potential drop near the grid.
Since the beam edges both radially and at large distances
downstream are also at lower potentials, an electron trap is
formed. This trap causes the electrons emitted from the
neutralizer to rebound from the beam boundaries and contains
them long enough so that their energies are randomized
through collision effects15. This is the reason the electrons
present in the beam plasma usually exhibit a maxwellian
distribution.
V
neutralizer
distance along
accelerator beam axis
Figure 2.6-1 Potential Variation In The Beam
29
III. PLASMA DIAGNOSTICS USING LANGMUIR PROBES
3.1 Basic Probe Theory
The Langmuir probe is basically an electrode inserted
into a plasma whose potential with respect to the plasma
may be varied. A current of charged particles is collected
by the probe with the current magnitude and type of parti-
cle collected determined by the probe's relative potential.
A plot of collected current, IP, versus probe potential, VP,is called the probe "characteristic". An ideal probe charac-
teristic is shown in Figure 3.1-1 for an electron-positive
ion plasma with both species possessing Maxwellian energy
distributions. For the purposes of this study, electron
I P0
070 O S VP
Figure 3.1-1 Ideal Probe Characteristic
current will be considered positive. When the probe is
biased sufficiently negative (region A), the probe will repel
all electrons and collect only ions intersecting the probe
sheath. For a thin sheath, this current is equal to:
I = !ZeAgn+ 4 (3.1)
where Z is the ion charge multiplier (Z=1 for singly charged
ions), AP is the probe collection area, and c+ is the average
ion speed. The average speed for a charged particle in a
30
Maxwellian distribution is given by:
1
c = (8kT/im) 2 (3.2)
where T is the species temperature and m is the particle
mass. In region B, the probe collects both ions and electrons
so that the probe current is:
Ip = eAp[neceexp(-e(VS-Vp)/kT e)
-Zn+C+l (3'3)
where ne is the electron density, Te is the electron temper-
ature, and me is the electron mass. The plasma potential is
usually found by locating the bend in the characteristic as
shown. At the point VP = VOC, the electron and ion currents
to the probe are equal. This is the zero current potential.
In region C, the current to the probe is equal to:
p= eAPnece (3.4)
since all ions are repelled at a few volts above VS for the
typical plasma in which Te is much higher than T+. It should
be remembered that these results apply to the thin sheath
case.
The actual characteristic observed in this study is
as shown in Figure 3.1-2. Neither ion nor electron sat-
uration occurs. This may be due to several causes. First
of all, as the probe is biased higher or lower than VS, the
sheath grows in thickness thereby increasing the probe's
effective collection area. Ssecondly, if the probe is nega-
tive with respect to the plasma, the ions are accelerated
within the sheath and acquire high kinetic energies. Upon
impact on the probe surface, the ions cause electrons to be
emitted into the plasma. This process is known as secondary
emission and effectively multiplies the ion current by a
31
IP
V ITS P
Figure 3.1-2 Typical Probe Characteristic
factor called the secondary emission coefficient. As an
example, the values of this secondary coefficient for singly
charged argon ion impact on tungsten are given in Table
3.1-1 . It was also found'7 that in the presence of a high
velocity flowing plasma, a probe biased positive with respect
to VS is not shielded by a plasma sheath. A wake is created
and a region in which the potential is higher than that of
the probe may be created upstream from the probe.
Table 3.1-1 Secondary Emission Coefficient For
Argon Ion Impact On Tungsten
Ion energy(keV) 0.01 0.03 0.10 0.30 1.00
Coefficient 0.035 0.040 0.045 0.058 0.075
32
3.2 Determination of ne, Te, and VS
In spite of the above complications, it is still
possible to determine VS. Making the appropriate assumptions,
ne and Te may then be determined. Figure 3.2-1 shows a typi-
cal semi-log plot of probe current density, jp(=TP/Ap),
versus V . Over most of the electron repelling-positive ion
attracting region, the electron current is much greater than
the ion current due to the higher electron temperature and
lower mass. Neglecting the ion contribution and converting
to current density, (3.3) becomes:
jp = 'eneceexp[-e(V 5-Vp)/kT(
Taking the natural log of (3.5) yields:
ln jp = ln( enec,) - e(V -Vp)/kT, (3.6)
Since ,en c and e/kT are constants (assumed), (3.6) is
the equation of a straight line of slope e/kTe. Returning
to Figure 3.2-1, it can be seen that A is the region in
which the ion current becomes important while B is the elec-
tron dominant region corresponding to (3.6). For Te> T+ in
the electron attracting region (Vp> VS), the probe field does
work on the electrons apparently increasing their tempera-18
ture . This would serve to decrease the slope of the line
which occurs in region C. Therefore, drawing two best-fit
lines through the data points yields VS as the intersection
point. The inverse of the slope in region B gives the elec-
tron temperature:
Te = e/km (3.7)
where m is the slope usually written as m = d(ln j)/dV. The
intersection of the lines also gives the natural log of the
electron saturation current (neglecting the ion contribution)
33
and with Te available makes the determination of ne possible.
From (3.2) and (3.4), the density is found to be:
1n e = je (saturation)/e x [21me/kT el- (3.8)
where je is the electron current density and will be assumed
to be equal to jp at Vs. It will also be assumed that ne is
equal to nm since np/nm is usually small.
ln j. I
-.
0.~*~
.0
VS VP
Figure 3.2-1 Typical Semi-log Plot of Probe Current
Density vs. Probe Potential
34
3.3 Effect of Ion Beam On Probe Response
Two probes were used in this study. One was inserted
into the discharge chamber. The other was placed in the beam
plasma. The effect of the beam was to increase the rounding
of the semi-log plot (region A in Fig. 3.2-1). This made the
fit of a straight line fairly difficult. However, it was
still possible to locate three or more collinear points
near the break. Also, the data points comprising region C
were easy to locate.
Segall and Koopman1 7 have found that if the Debye
length, ND, is less than the probe radius, R, and if ce ismuch greater than the beam velocity, then the electron
current is approximately:
I = eAPnece exp[-e(VS-Vp)/kTel (3.9)
and that the probe collects electrons primarily on the
surface facing the beam so that:
AP =TTRL (3.10)
where L is the probe length (cylindrical probe). The Debye
length is a measure of the dimension over which thermal
energy affects plasma neutrality and is equal to1 9:
2 1-ND = (eokT/e ne)2 (3.11)
where e0 is the permittivity of free space. From the results
of this study, ND was found to have a value of several milli-
meters as compared to a probe radius of 0.3 mm. Thus, the
probe was operated outside of the regime described above.
However, with no prior knowledge as to the actual probe
collection area, equation (3.10) was assumed to still be
valid. This leads to a possible maximum error of 200 % in
the determination of the electron density.
35
For a thin sheath, the ion current to the probe is
basically that portion of the beam intercepted by the probe.
This current is equal to:
I+ = eUAn n+. (3.12)
where A in this case is the area projected normal to the
beam and is equal to 2RL for a cylindrical probe mounted
transverse to the beam. The ion current was not accounted
for in determining ne, Te, and VS since it was found to be
somewhat less than the electron current at the plasma
potential. This would result in a high estimate of Tel? and
a low estimate of ne.
36
3.4. Effect of Negative Ions On Probe Response
As previously mentioned, the oxygen plasma may possess
a negative ion density which is many times higher than the
electron density. However, if the temperature of the nega-
tive and positive ions is small as compared to the electron
temperature, their effect on probe response may be neglected.
This can best be illustrated using values obtained from
this study. For the purposes of this exercise, a thin sheath
will be assumed.
At the plasma potential, the probe collects a current
which is equal to:
P= eAp(nece+n-c--n+c+) (3.13)
where the -subscript "-" indicates negative ions. This will
basically be of the type 0~. The temperature of the ions
is basically that of the chamber walls and is estimated to
be about 6000 K. A typical electron temperature in the
chamber is 348,0000 K (or 30 eV) while the electron density
was about 5x1015 M-3. Using (3.2), the quantity nece is
found to equal 1.83x1022 m-2 .s-1. For a positive ion to
electron density ratio of 10 (i.e. n+=5x10 i6 m 3 ), n+c+is found to equal 3.15x10 19 m-2 .s-1 yielding an electron
to positive ion current ratio of 581. It is assumed that the
negative ion temperature is of the same magnitude as that of
the positive ions and certainly much less than the electron
temperature. Taking T_ = T+ = 6000 K and a negative ion to
electron density ratio of 9 (from plasma neutrality), n-c-
is found to equal 4.01x1019 m- 2s-1 or 0.22% of the electron
contribution at VP = VS. Of course, at VS, the negative and
positive ion contributions, being of opposite sign, tend to
cancel each other out. In the electron repelling-positive
ion attracting region in which the plasma properties are
computed (region B in Fig. 3.2-1), the effects of the
negative ions are negligible. When the probe is biased only
37
a few volts negative with respect to the plasma, the low
temperature negative ions are almost totally repelled.
38
3.5 Sheath Thickness
The approximate thickness of the sheath in the elec-
tron repelling-ion attracting region may be found using the
familiar Child-Langmuir Law for space-charge limited ion
current between two electrodes at different potentials:
j+ = 4e0V1.5(2e/m)2 /9L2 (3.14)
where V is the potential difference and L is the inter-
electrode spacing. If the probe and sheath radii are of the
same magnitude (See Fig. 3.5-1), then their surfaces may be
approximated as flat electrodes. L then becomes the sheath
thickness, 1s. The sheath has to conduct all the ions inter-
cepting it so that j= ien c+. Inserting this and (3.2) into
(3.14) and solving for 1s yields:
1= [8e0(T/ekT+)(V SV P)1.5/9n+1 (3.15)
Taking into account the fact that the modified Bohm velocity
derived in Section 2.3 yields values which are slightly
lower than c+, it would be expected that the sheath is
slightly thicker than predicted by (3.15). However, (3.15)
still serves as a good estimate. Boyd and Thompson20 conclu-
ded that for a highly electronegative plasma with T_~ T+
the probe collection area approaches the sheath surface area
in the case of a spherical probe.
probe
lsR
sheath
Figure 3.5-1 Sheath Formation On A Langmuir Probe
39
3.6 Orbital Motion LimitMuch of the theory presented above assumes a thin
sheath. However, as previously mentioned, the sheath conti-
nues to grow in thickness as the probe potential is lowered
with respect to the plasma. A point is reached at which not
all the particles entering the sheath are collected. Some
particles of sufficient energy enter the sheath but escape
the probe's influence. The theory of orbital motion limit
(OML) analyzes the phenomenon assuming a very thick sheath.
Using energy and momentum conservation, it is possible to
determine the energy at which capture occurs. All particles
possessing lower energies are captured while those possessing
higher energies escape. The number of particles collected
can then be found by using the energy distribution function
and integrating from zero to the capture energy. The results
in the positive ion attracting region have been found to
be18,
I+ = APn+e(2kT+m+)2/{ (Xp) 2.1
+ i(i)2exp(Xp)(1-erf(Xp2))J (3.16a)
I = IAneceexp(-X*) (3.16b)
for electrons and ions with Maxwellian energy distributions.
The quantities Xp and X* are equal to e(V -V )/kT and
e(V -VP)/kTe respectively. Erf is the error function.
40
3.7 Effect of Magnetic Field On Probe Response
The effect of the magnetic field may be considered
negligible if the Larmor radius, rL, is larger than both R
and ND 18. The Larmor radius is the radius of the circular
trajectory described by a charged particle in a magnetic
field and is equal to:
rL = mvt/ZeB (3.17)
where B is the magnetic field strength and vt is the tan-
gential velocity. Taking the tangential velocity to be the
thermal velocity given by (3.2) and a field strength of
2.04 x 10~3 Tesla, the following values are obtained:
rLe = 10.2 mm
rL+ = 102.6 mm
ND = 0.58 mm
R = 0.13 mm
The field strength chosen is typical of that present in the
vicinity of the probe for many of-the runs made in this
study. Te was taken to be 30 eV, ne was taken to be 5 x 1015
m~3, and T+ was assumed to be 6000 K. Thus, the'effects of
the magnetic field may be neglected over the general range
of this study.
41
IV. APPARATUS AND PROCEDURE
4.1 Engine Construction
The engine is constructed as shown in Figure 4.1-1.
The aluminum outer body serves to keep the magnetic field
windings cool. It is 11.4 cm long with an outer diameter of
10.2 cm and is 2.38 mm thick. The magnetic field is produced
by turns of insulated wire mounted as shown in Figure 4.1-2.
The anode is made of steel and is mounted on three ceramic
insulators attached to the outer body. It is 10.5 cm long,
1.59 mm thick, and has an outer diameter of 6.35 cm. The
backplate is made of 0.51 mm thick steel plate and is
supported by screws attached to the outer body. Sealing is
accomplished by a fillet of silicone rubber around the outer
edge. A ceramic plug serves as the cathode mount. Two 0.635
mm diameter tungsten rods pass through holes drilled in the
ceramic plug. Spotwelded to the tungsten feeds is the ca-
thode filament which is a 1.02 x 0.05 mm tungsten ribbon.
The screen and accelerator grids were supplied by the
Jet Propulsion Laboratory and are identical. They are 11.4 cm
in diameter and 1.02 mm thick. There are 211 holes machined
into the grids, each with a diameter of 4.76 mm. The open
area fraction is approximately 0.464. The grids are sand-
wiched between aluminum brackets and are kept separated by
small ceramic rings (See Fig. 4.1-1, close-up). The space
between the grids is approximately 2 mm.
The neutralizer is a 0.25 mm diameter tungsten wire
spotwelded to 0.635 mm tungsten feeds. These pass through
a ceramic block supported by a clamp. The neutralizer is
located several centimeters below the engine.
The engine and neutralizer are mounted on a metal test
stand. The neutralizer is held by a clamp while the engine
is mounted on an aluminum bracket. An integral part of the
engine mounting bracket is a ceramic spacer which electrical-
ly insulates the engine from the test stand.
42
accelerator grid
screen grid
backplate
ceramicholder
LI-VW~J~
annoDo
Do
cathode
baffle
ano
go
de onan
'no
magnetic field windings
ceramic spacer (3)
Figure 4.1-1 Ion Engine Cross Section
5 turns
4 turns
1 t urn
I I
Figure 4.1-2 Magnetic FieldWinding Configuration
43
j
cathodefeed
ngas
Teflon
sleeve
4.2 Electrical System
Electrical power to the engine is supplied by one AC
and several DC power supplies. The configuration and speci-
fications are shown in Figure 4.2-1. Voltage and current
readings were made primarily with a digital multimeter
(Keithley Model 169). Its accuracy is listed as + 0.25%(voltage) and 1.5%(current) by its manufacturer. It was used
to measure the anode collection current (IA), neutralizer
emission current (IN), accelerator grid impingement current
(IG ) and the cathode emission current (IC). The reference
voltage (VR), anode voltage (VA), and magnetic field current
(IBF) were read from the power supply meters and were found
to have accuracies of + 1%, ± 3%, and 1 2% respectively.
4.3 Langmuir Probe System
The probes were constructed using tungsten as the
collection material to reduce secondary emission effects.
The chamber probe is a length of 0.254 mm tungsten wire
inserted in a 1-57 mm diameter ceramic tube. The stream
probe is a 0.635 mm diameter tungsten rod inserted in a
1.45 mm diameter ceramic tube. The tungsten collectors are
spotwelded to nickel which is in turn soldered to insulated
wire which leads to an electrical jack in the base of the
vacuum chamber. The tungsten-nickel-wire joint is shielded
with heat shrink tubing.
The electrical configuration is shown in Figure 4.3-1.The chamber probe is referenced to the anode while the stream
probe is referenced to ground. The probe potential, VP, was
measured using an electromechanical voltmeter while the
probe current, IP, was measured using the multimeter de-
scribed in Section 4.2. The electromechanical voltmeter
was found to be accurate to within + 1 V up to 100 V and
t 5 V up to 200 V. The potential was manually varied.
44
+
50 V 300 V v 500 V60 A 5 A O.2 A
120 V
600 V
0.3 A
Figure 4.2-1 Power Supply Configuration
45
chamber
anodeprobes
O' groundstream
polarity switch
iP
300 v0.2 A
Figure 4.3-1 Langmuir Probe System
46
4.4 Vacuum Chamber and Propellant Feed System
The engine is located in a small vacuum chamber. Withmechanical and diffusion pumps in series, pressures of approx-imately two microtorr are achievable with no gas flow. Thechamber is about 0.7 m tall, 0.45 m in diameter, and enclosesa volume of about 0.12 m. An ionization pressure gauge wasused to measure the pressure in the chamber. With gas flow,
the pressure rose to the upper 10-6 to lower 10-5 torr range.The propellant feed system is as shown in Figure 4.4-1.
Propellant was supplied from a high pressure gas cylinder. Apressure regulator was used to feed a micrometering valve atslightly higher than one atmosphere inlet pressure as
measured with a mechanical pressure gauge. A vernier controldetermines the flowrate to the thruster. Plastic tubing wasused outside the chamber while copper tubing was used inside.A 3.18 mm (i.d.) copper tube was connected to a 3.18 mm(i.d.) steel tube by way of a Teflon sleeve (See Fig.4.1-1).The sleeve served to electrically insulate the engine bodyfrom the feed system which is grounded. The steel tube entersthe discharge chamber through the backplate. A baffle madeof a metal ring and wire screen was used to distribute thegas.